Multivariate Regularized Newton and Levenberg-Marquardt methods: a comparison on synthetic data of tumor hypoxia in a kinetic framework

• Main Authors: Garbarino Sara, Caviglia Giacomo
• Format: Article
• Language: English
• Published: Sciendo 2019-01-01
• Series: Communications in Applied and Industrial Mathematics
• Subjects: compartmental analysis; newton methods; tumor hypoxia; fmiso-pet
• Online Access: https://doi.org/10.2478/caim-2019-0006

In this paper we propose a new algorithm to optimize the parameters of a compartmental problem describing tumor hypoxia. The method is based on a multivariate Newton approach, with Tikhonov regularization, and can be easily applied to data with diverse statistical distributions. Here we simulate [18F]−fluoromisonidazole Positron Emission Tomography dynamic data of hypoxia of a neck tumor and describe the tracer flow inside tumor with a two-compartments compartmental model. We perform optimization on the parameters of the model via the proposed Multivariate Regularized Newton method and validate it against results obtained with a standard Levenberg-Marquardt approach. The proposed algorithm returns parameters that are closer to the ground truth while preserving the statistical distribution of the data.